A Google blog post detailing the relationship between Pokemon Go and the Google Cloud goes some way to explaining the game's stop-start launch.
The augmented reality Pokemon sim utilizes various Google Cloud features, but it's the Google Cloud Datastore that serves as the primary database for the game's many Pokemon captures. As such, it's one of the best ways to measure the title's overall popularity.
In the lead up to launch Niantic set themselves a "launch target" for player traffic, but just in case things got out of hand, they also made sure to prep the Datastore for a "worst case" scenario.
In this case, Niantic saw that worst case scenario as traffic levels five times higher than their original target.
As shown in the graph below, however, even that turned out to be a conservative estimate, with traffic quickly surging to fifty times Niantic's original target. Taking that into account, it's no surprise the studio failed to keep their servers online as they rolled out Pokemon Go around the world.